Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T12:48:59.508Z Has data issue: false hasContentIssue false
  • English
  • Français

A Unified View of the Law of the Wall Using Mixing-Length Theory

Published online by Cambridge University Press:  07 June 2016

V C Patel
V C Patel*
Affiliation:
Institute of Hydraulic Research, University of Iowa
Get access

Summary

It is shown that, if the well-known mixing-length formula is regarded simply as a relationship between the velocity and the stress distributions in the wall region of a turbulent flow, then a truly universal distribution of mixing length is sufficient to describe the experimentally observed departures of the velocity distribution from the usual law of the wall as a result of severe pressure gradients and transverse surface curvature. Comparisons have been made with a wide variety of experimental data to demonstrate the general validity of the mixing-length model in describing the flow close to a smooth wall.

An extension of the re-laminarisation criterion of Patel and Head, and some experimental evidence, suggest that the thick axisymmetric boundary layer on a slender cylinder placed axially in a uniform stream cannot be maintained in a fully turbulent state for values of the Reynolds number, based on friction velocity and cylinder radius, below a certain critical value.

Type
Research Article
Information
Aeronautical Quarterly , Volume 24 , Issue 1 , February 1973 , pp. 55 - 70
Copyright
Copyright © Royal Aeronautical Society. 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Batchelor, G K Note on free turbulent flows, with special reference to the two-dimensional wake. Journal of the Aeronautical Sciences, Vol 17, p 441, 1950.CrossRefGoogle Scholar
2 Patel, V C Head, M R Reversion of turbulent to laminar flow. Journal of Fluid Mechanics, Vol 34, p 371, 1968.CrossRefGoogle Scholar
3 Patel, V C Calibration of the Preston tube and limitations on its use in pressure gradients. Journal of Fluid Mechanics, Vol 23, p 185, 1965.CrossRefGoogle Scholar
4 Reichardt, H Vollständige Darstelling der turbulenten Geschwindigkeitsverteilung in glatten Leitungen. Zeitschrift für Angewandte Mathematik und Mechanik, Vol 31, p 208, 1951.CrossRefGoogle Scholar
5 Deissler, R G Analysis of turbulent heat transfer, mass transfer and friction in smooth tubes at high Prandtl and Schmidt numbers. NACA Technical Report 1210, 1954.Google Scholar
6 van Driest, E R On turbulent flow near a wall. Journal of the Aeronautical Sciences, Vol 23, pp 1007 and 1036, 1956.CrossRefGoogle Scholar
7 Stratford, B S The prediction of separation of the turbulent boundary layer. Journal of Fluid Mechanics, Vol 5, p 1, 1959.CrossRefGoogle Scholar
8 Townsend, A A Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol 11, p 97, 1961.CrossRefGoogle Scholar
9 McDonald, H The effect of pressure gradient on the law of the wall in turbulent flow. Journal of Fluid Mechanics, Vol 35, p 311, 1969.CrossRefGoogle Scholar
10 Patel, V C Contributions to the study of turbulent boundary layers. PhD Thesis, Cambridge University, England, 1965.Google Scholar
11 Mellor, G L The effects of pressure gradients on turbulent boundary layers. Journal of Fluid Mechanics, Vol 24, p 255, 1966.CrossRefGoogle Scholar
12 Newman, B G Some contributions to the study of the turbulent boundary layer. Australian Department of Supply, Report ACA-53, 1951.Google Scholar
13 Head, M R Rechenberg, I The Preston tube as a means of measuring skin friction. Journal of Fluid Mechanics, Vol 14, p 1, 1962.CrossRefGoogle Scholar
14 Patel, V C Head, M R Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. Journal of Fluid Mechanics, Vol 38, p 181, 1969.CrossRefGoogle Scholar
15 Rao, G N V The law of the wall in a thick axisymmetric turbulent boundary layer. Journal of Basic Engineering, Transactions ASME, Series D, Vol 89, p 237, 1967.CrossRefGoogle Scholar
16 Rothfus, R R Monrad, C C Senecal, V E Velocity distribution and fluid friction in smooth concentric annuii. Industrial and Engineering Chemistry, Vol 42, p 2511, 1950.CrossRefGoogle Scholar
17 Owen, W M Experimental study of water flow in annular pipes. Proceedings ASCE, Vol 77, Separate No. 88, 1951.Google Scholar
18 Knudsen, J G Katz, D L Velocity profiles in annuii. Proceedings of Midwestern Conference on Fluid Mechanics, 1950.Google Scholar
19 Brighton, J A Jones, J B Fully developed turbulent flow in annuii. Journal of Basic Engineering, Transactions ASME, Series D, Vol 86, p 835, 1964.CrossRefGoogle Scholar
20 Quarmby, A An experimental study of turbulent flow through concentric annuii. International Journal of Mechanical Sciences, Vol 9, p 205, 1967.CrossRefGoogle Scholar
21 Levy, S Turbulent flow in an annulus. Journal of Heat Transfer, Transactions ASME, Vol 89, p 25, 1967.CrossRefGoogle Scholar
22 Lawn, C J Elliott, C J Fully developed turbulent flow through concentric annuii. Central Electricity Generating Board, Berkeley, England, Report RD/B/N1878, 1971.Google Scholar
23 Richmond, R L Experimental investigation of thick axially symmetric boundary layers on cylinders at subsonic and hypersonic speeds. PhD Thesis, California Institute of Technology, Pasadena, 1957.Google Scholar
24 Yu, Y S Effect of transverse curvature on turbulent boundary layer characteristics. Journal of Ship Research, Vol 3, p 33, 1958.CrossRefGoogle Scholar
25 Yasuhara, M Experiments of axisymmetric boundary layers along a cylinder in incompressible flow. Transactions, Japan Society for Aerospace Science, Vol 2, p 33, 1959.Google Scholar
26 Keshavan, N R Axisymmetric incompressible turbulent boundary layers in zero pressure gradient flow. MSc Thesis, Indian Institute of Science, Bangalore, India, 1969.Google Scholar
27 Willmarth, W W Yang, C S Wall-pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder. Journal of Fluid Mechanics, Vol 41, p 47, 1970.CrossRefGoogle Scholar
28 Landweber, L Effect of transverse curvature on frictional resistance. David Taylor Model Basin Report 689, 1949.Google Scholar
29 Cebeci, T Laminar and turbulent incompressible boundary layers on slender bodies of revolution in axial flow. Journal of Basic Engineering, Transactions ASME Series D, Vol 92, p 545, 1970.CrossRefGoogle Scholar
30 Clauser, F H The turbulent boundary layer. Advances in Applied Mechanics, Vol 4, p 1, 1956.CrossRefGoogle Scholar
31 White, F M Written discussion of the paper of Cebeci. Journal of Basic Engineering, Transactions ASME, Vol 92, p 550, 1970.CrossRefGoogle Scholar